doc-src/IsarImplementation/Thy/prelim.thy
author wenzelm
Mon Mar 12 19:23:48 2007 +0100 (2007-03-12)
changeset 22438 96e650157b1e
parent 21862 13e9febe3080
child 22869 9f915d44a666
permissions -rw-r--r--
tuned;
wenzelm@18537
     1
wenzelm@18537
     2
(* $Id$ *)
wenzelm@18537
     3
wenzelm@18537
     4
theory prelim imports base begin
wenzelm@18537
     5
wenzelm@18537
     6
chapter {* Preliminaries *}
wenzelm@18537
     7
wenzelm@20429
     8
section {* Contexts \label{sec:context} *}
wenzelm@18537
     9
wenzelm@20429
    10
text {*
wenzelm@20451
    11
  A logical context represents the background that is required for
wenzelm@20451
    12
  formulating statements and composing proofs.  It acts as a medium to
wenzelm@20451
    13
  produce formal content, depending on earlier material (declarations,
wenzelm@20451
    14
  results etc.).
wenzelm@18537
    15
wenzelm@20451
    16
  For example, derivations within the Isabelle/Pure logic can be
wenzelm@20451
    17
  described as a judgment @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<phi>"}, which means that a
wenzelm@20429
    18
  proposition @{text "\<phi>"} is derivable from hypotheses @{text "\<Gamma>"}
wenzelm@20429
    19
  within the theory @{text "\<Theta>"}.  There are logical reasons for
wenzelm@20451
    20
  keeping @{text "\<Theta>"} and @{text "\<Gamma>"} separate: theories can be
wenzelm@20451
    21
  liberal about supporting type constructors and schematic
wenzelm@20451
    22
  polymorphism of constants and axioms, while the inner calculus of
wenzelm@20451
    23
  @{text "\<Gamma> \<turnstile> \<phi>"} is strictly limited to Simple Type Theory (with
wenzelm@20451
    24
  fixed type variables in the assumptions).
wenzelm@18537
    25
wenzelm@20429
    26
  \medskip Contexts and derivations are linked by the following key
wenzelm@20429
    27
  principles:
wenzelm@20429
    28
wenzelm@20429
    29
  \begin{itemize}
wenzelm@20429
    30
wenzelm@20429
    31
  \item Transfer: monotonicity of derivations admits results to be
wenzelm@20451
    32
  transferred into a \emph{larger} context, i.e.\ @{text "\<Gamma> \<turnstile>\<^sub>\<Theta>
wenzelm@20451
    33
  \<phi>"} implies @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta>\<^sub>' \<phi>"} for contexts @{text "\<Theta>'
wenzelm@20451
    34
  \<supseteq> \<Theta>"} and @{text "\<Gamma>' \<supseteq> \<Gamma>"}.
wenzelm@18537
    35
wenzelm@20429
    36
  \item Export: discharge of hypotheses admits results to be exported
wenzelm@20451
    37
  into a \emph{smaller} context, i.e.\ @{text "\<Gamma>' \<turnstile>\<^sub>\<Theta> \<phi>"}
wenzelm@20451
    38
  implies @{text "\<Gamma> \<turnstile>\<^sub>\<Theta> \<Delta> \<Longrightarrow> \<phi>"} where @{text "\<Gamma>' \<supseteq> \<Gamma>"} and
wenzelm@20451
    39
  @{text "\<Delta> = \<Gamma>' - \<Gamma>"}.  Note that @{text "\<Theta>"} remains unchanged here,
wenzelm@20451
    40
  only the @{text "\<Gamma>"} part is affected.
wenzelm@20429
    41
wenzelm@20429
    42
  \end{itemize}
wenzelm@18537
    43
wenzelm@20451
    44
  \medskip By modeling the main characteristics of the primitive
wenzelm@20451
    45
  @{text "\<Theta>"} and @{text "\<Gamma>"} above, and abstracting over any
wenzelm@20451
    46
  particular logical content, we arrive at the fundamental notions of
wenzelm@20451
    47
  \emph{theory context} and \emph{proof context} in Isabelle/Isar.
wenzelm@20451
    48
  These implement a certain policy to manage arbitrary \emph{context
wenzelm@20451
    49
  data}.  There is a strongly-typed mechanism to declare new kinds of
wenzelm@20429
    50
  data at compile time.
wenzelm@18537
    51
wenzelm@20451
    52
  The internal bootstrap process of Isabelle/Pure eventually reaches a
wenzelm@20451
    53
  stage where certain data slots provide the logical content of @{text
wenzelm@20451
    54
  "\<Theta>"} and @{text "\<Gamma>"} sketched above, but this does not stop there!
wenzelm@20451
    55
  Various additional data slots support all kinds of mechanisms that
wenzelm@20451
    56
  are not necessarily part of the core logic.
wenzelm@18537
    57
wenzelm@20429
    58
  For example, there would be data for canonical introduction and
wenzelm@20429
    59
  elimination rules for arbitrary operators (depending on the
wenzelm@20429
    60
  object-logic and application), which enables users to perform
wenzelm@20451
    61
  standard proof steps implicitly (cf.\ the @{text "rule"} method
wenzelm@20451
    62
  \cite{isabelle-isar-ref}).
wenzelm@18537
    63
wenzelm@20451
    64
  \medskip Thus Isabelle/Isar is able to bring forth more and more
wenzelm@20451
    65
  concepts successively.  In particular, an object-logic like
wenzelm@20451
    66
  Isabelle/HOL continues the Isabelle/Pure setup by adding specific
wenzelm@20451
    67
  components for automated reasoning (classical reasoner, tableau
wenzelm@20451
    68
  prover, structured induction etc.) and derived specification
wenzelm@20451
    69
  mechanisms (inductive predicates, recursive functions etc.).  All of
wenzelm@20451
    70
  this is ultimately based on the generic data management by theory
wenzelm@20451
    71
  and proof contexts introduced here.
wenzelm@18537
    72
*}
wenzelm@18537
    73
wenzelm@18537
    74
wenzelm@18537
    75
subsection {* Theory context \label{sec:context-theory} *}
wenzelm@18537
    76
wenzelm@20429
    77
text {*
wenzelm@20447
    78
  \glossary{Theory}{FIXME}
wenzelm@20447
    79
wenzelm@20451
    80
  A \emph{theory} is a data container with explicit named and unique
wenzelm@20451
    81
  identifier.  Theories are related by a (nominal) sub-theory
wenzelm@20451
    82
  relation, which corresponds to the dependency graph of the original
wenzelm@20451
    83
  construction; each theory is derived from a certain sub-graph of
wenzelm@20451
    84
  ancestor theories.
wenzelm@20451
    85
wenzelm@20451
    86
  The @{text "merge"} operation produces the least upper bound of two
wenzelm@20451
    87
  theories, which actually degenerates into absorption of one theory
wenzelm@20451
    88
  into the other (due to the nominal sub-theory relation).
wenzelm@18537
    89
wenzelm@20429
    90
  The @{text "begin"} operation starts a new theory by importing
wenzelm@20429
    91
  several parent theories and entering a special @{text "draft"} mode,
wenzelm@20429
    92
  which is sustained until the final @{text "end"} operation.  A draft
wenzelm@20451
    93
  theory acts like a linear type, where updates invalidate earlier
wenzelm@20451
    94
  versions.  An invalidated draft is called ``stale''.
wenzelm@20429
    95
wenzelm@20447
    96
  The @{text "checkpoint"} operation produces an intermediate stepping
wenzelm@20451
    97
  stone that will survive the next update: both the original and the
wenzelm@20451
    98
  changed theory remain valid and are related by the sub-theory
wenzelm@20451
    99
  relation.  Checkpointing essentially recovers purely functional
wenzelm@20451
   100
  theory values, at the expense of some extra internal bookkeeping.
wenzelm@20447
   101
wenzelm@20447
   102
  The @{text "copy"} operation produces an auxiliary version that has
wenzelm@20447
   103
  the same data content, but is unrelated to the original: updates of
wenzelm@20447
   104
  the copy do not affect the original, neither does the sub-theory
wenzelm@20447
   105
  relation hold.
wenzelm@20429
   106
wenzelm@20447
   107
  \medskip The example in \figref{fig:ex-theory} below shows a theory
wenzelm@20451
   108
  graph derived from @{text "Pure"}, with theory @{text "Length"}
wenzelm@20451
   109
  importing @{text "Nat"} and @{text "List"}.  The body of @{text
wenzelm@20451
   110
  "Length"} consists of a sequence of updates, working mostly on
wenzelm@20451
   111
  drafts.  Intermediate checkpoints may occur as well, due to the
wenzelm@20451
   112
  history mechanism provided by the Isar top-level, cf.\
wenzelm@20451
   113
  \secref{sec:isar-toplevel}.
wenzelm@20447
   114
wenzelm@20447
   115
  \begin{figure}[htb]
wenzelm@20447
   116
  \begin{center}
wenzelm@20429
   117
  \begin{tabular}{rcccl}
wenzelm@20447
   118
        &            & @{text "Pure"} \\
wenzelm@20447
   119
        &            & @{text "\<down>"} \\
wenzelm@20447
   120
        &            & @{text "FOL"} \\
wenzelm@18537
   121
        & $\swarrow$ &              & $\searrow$ & \\
wenzelm@21852
   122
  @{text "Nat"} &    &              &            & @{text "List"} \\
wenzelm@18537
   123
        & $\searrow$ &              & $\swarrow$ \\
wenzelm@20447
   124
        &            & @{text "Length"} \\
wenzelm@18537
   125
        &            & \multicolumn{3}{l}{~~$\isarkeyword{imports}$} \\
wenzelm@18537
   126
        &            & \multicolumn{3}{l}{~~$\isarkeyword{begin}$} \\
wenzelm@18537
   127
        &            & $\vdots$~~ \\
wenzelm@20447
   128
        &            & @{text "\<bullet>"}~~ \\
wenzelm@20447
   129
        &            & $\vdots$~~ \\
wenzelm@20447
   130
        &            & @{text "\<bullet>"}~~ \\
wenzelm@20447
   131
        &            & $\vdots$~~ \\
wenzelm@18537
   132
        &            & \multicolumn{3}{l}{~~$\isarkeyword{end}$} \\
wenzelm@20429
   133
  \end{tabular}
wenzelm@20451
   134
  \caption{A theory definition depending on ancestors}\label{fig:ex-theory}
wenzelm@20447
   135
  \end{center}
wenzelm@20447
   136
  \end{figure}
wenzelm@20451
   137
wenzelm@20451
   138
  \medskip There is a separate notion of \emph{theory reference} for
wenzelm@20451
   139
  maintaining a live link to an evolving theory context: updates on
wenzelm@20488
   140
  drafts are propagated automatically.  Dynamic updating stops after
wenzelm@20488
   141
  an explicit @{text "end"} only.
wenzelm@20451
   142
wenzelm@20451
   143
  Derived entities may store a theory reference in order to indicate
wenzelm@20451
   144
  the context they belong to.  This implicitly assumes monotonic
wenzelm@20451
   145
  reasoning, because the referenced context may become larger without
wenzelm@20451
   146
  further notice.
wenzelm@18537
   147
*}
wenzelm@18537
   148
wenzelm@20430
   149
text %mlref {*
wenzelm@20447
   150
  \begin{mldecls}
wenzelm@20447
   151
  @{index_ML_type theory} \\
wenzelm@20447
   152
  @{index_ML Theory.subthy: "theory * theory -> bool"} \\
wenzelm@20447
   153
  @{index_ML Theory.merge: "theory * theory -> theory"} \\
wenzelm@20447
   154
  @{index_ML Theory.checkpoint: "theory -> theory"} \\
wenzelm@20547
   155
  @{index_ML Theory.copy: "theory -> theory"} \\
wenzelm@20547
   156
  \end{mldecls}
wenzelm@20547
   157
  \begin{mldecls}
wenzelm@20447
   158
  @{index_ML_type theory_ref} \\
wenzelm@20447
   159
  @{index_ML Theory.self_ref: "theory -> theory_ref"} \\
wenzelm@20447
   160
  @{index_ML Theory.deref: "theory_ref -> theory"} \\
wenzelm@20447
   161
  \end{mldecls}
wenzelm@20447
   162
wenzelm@20447
   163
  \begin{description}
wenzelm@20447
   164
wenzelm@20451
   165
  \item @{ML_type theory} represents theory contexts.  This is
wenzelm@20451
   166
  essentially a linear type!  Most operations destroy the original
wenzelm@20451
   167
  version, which then becomes ``stale''.
wenzelm@20447
   168
wenzelm@20447
   169
  \item @{ML "Theory.subthy"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
wenzelm@20447
   170
  compares theories according to the inherent graph structure of the
wenzelm@20447
   171
  construction.  This sub-theory relation is a nominal approximation
wenzelm@20447
   172
  of inclusion (@{text "\<subseteq>"}) of the corresponding content.
wenzelm@20447
   173
wenzelm@20447
   174
  \item @{ML "Theory.merge"}~@{text "(thy\<^sub>1, thy\<^sub>2)"}
wenzelm@20447
   175
  absorbs one theory into the other.  This fails for unrelated
wenzelm@20447
   176
  theories!
wenzelm@20447
   177
wenzelm@20447
   178
  \item @{ML "Theory.checkpoint"}~@{text "thy"} produces a safe
wenzelm@20447
   179
  stepping stone in the linear development of @{text "thy"}.  The next
wenzelm@20447
   180
  update will result in two related, valid theories.
wenzelm@20447
   181
wenzelm@20447
   182
  \item @{ML "Theory.copy"}~@{text "thy"} produces a variant of @{text
wenzelm@20451
   183
  "thy"} that holds a copy of the same data.  The result is not
wenzelm@20451
   184
  related to the original; the original is unchanched.
wenzelm@20447
   185
wenzelm@20451
   186
  \item @{ML_type theory_ref} represents a sliding reference to an
wenzelm@20451
   187
  always valid theory; updates on the original are propagated
wenzelm@20447
   188
  automatically.
wenzelm@20447
   189
wenzelm@20449
   190
  \item @{ML "Theory.self_ref"}~@{text "thy"} and @{ML
wenzelm@20449
   191
  "Theory.deref"}~@{text "thy_ref"} convert between @{ML_type
wenzelm@20449
   192
  "theory"} and @{ML_type "theory_ref"}.  As the referenced theory
wenzelm@20449
   193
  evolves monotonically over time, later invocations of @{ML
wenzelm@20451
   194
  "Theory.deref"} may refer to a larger context.
wenzelm@20447
   195
wenzelm@20447
   196
  \end{description}
wenzelm@20430
   197
*}
wenzelm@20430
   198
wenzelm@18537
   199
wenzelm@18537
   200
subsection {* Proof context \label{sec:context-proof} *}
wenzelm@18537
   201
wenzelm@18537
   202
text {*
wenzelm@20447
   203
  \glossary{Proof context}{The static context of a structured proof,
wenzelm@20447
   204
  acts like a local ``theory'' of the current portion of Isar proof
wenzelm@20447
   205
  text, generalizes the idea of local hypotheses @{text "\<Gamma>"} in
wenzelm@20447
   206
  judgments @{text "\<Gamma> \<turnstile> \<phi>"} of natural deduction calculi.  There is a
wenzelm@20447
   207
  generic notion of introducing and discharging hypotheses.
wenzelm@20447
   208
  Arbritrary auxiliary context data may be adjoined.}
wenzelm@20429
   209
wenzelm@20447
   210
  A proof context is a container for pure data with a back-reference
wenzelm@20449
   211
  to the theory it belongs to.  The @{text "init"} operation creates a
wenzelm@20451
   212
  proof context from a given theory.  Modifications to draft theories
wenzelm@20451
   213
  are propagated to the proof context as usual, but there is also an
wenzelm@20451
   214
  explicit @{text "transfer"} operation to force resynchronization
wenzelm@20451
   215
  with more substantial updates to the underlying theory.  The actual
wenzelm@20451
   216
  context data does not require any special bookkeeping, thanks to the
wenzelm@20451
   217
  lack of destructive features.
wenzelm@20429
   218
wenzelm@20447
   219
  Entities derived in a proof context need to record inherent logical
wenzelm@20447
   220
  requirements explicitly, since there is no separate context
wenzelm@20447
   221
  identification as for theories.  For example, hypotheses used in
wenzelm@20451
   222
  primitive derivations (cf.\ \secref{sec:thms}) are recorded
wenzelm@20447
   223
  separately within the sequent @{text "\<Gamma> \<turnstile> \<phi>"}, just to make double
wenzelm@20447
   224
  sure.  Results could still leak into an alien proof context do to
wenzelm@20447
   225
  programming errors, but Isabelle/Isar includes some extra validity
wenzelm@22438
   226
  checks in critical positions, notably at the end of a sub-proof.
wenzelm@20429
   227
wenzelm@20451
   228
  Proof contexts may be manipulated arbitrarily, although the common
wenzelm@20451
   229
  discipline is to follow block structure as a mental model: a given
wenzelm@20451
   230
  context is extended consecutively, and results are exported back
wenzelm@20451
   231
  into the original context.  Note that the Isar proof states model
wenzelm@20451
   232
  block-structured reasoning explicitly, using a stack of proof
wenzelm@20451
   233
  contexts internally, cf.\ \secref{sec:isar-proof-state}.
wenzelm@18537
   234
*}
wenzelm@18537
   235
wenzelm@20449
   236
text %mlref {*
wenzelm@20449
   237
  \begin{mldecls}
wenzelm@20449
   238
  @{index_ML_type Proof.context} \\
wenzelm@20449
   239
  @{index_ML ProofContext.init: "theory -> Proof.context"} \\
wenzelm@20449
   240
  @{index_ML ProofContext.theory_of: "Proof.context -> theory"} \\
wenzelm@20449
   241
  @{index_ML ProofContext.transfer: "theory -> Proof.context -> Proof.context"} \\
wenzelm@20449
   242
  \end{mldecls}
wenzelm@20449
   243
wenzelm@20449
   244
  \begin{description}
wenzelm@20449
   245
wenzelm@20449
   246
  \item @{ML_type Proof.context} represents proof contexts.  Elements
wenzelm@20449
   247
  of this type are essentially pure values, with a sliding reference
wenzelm@20449
   248
  to the background theory.
wenzelm@20449
   249
wenzelm@20449
   250
  \item @{ML ProofContext.init}~@{text "thy"} produces a proof context
wenzelm@20449
   251
  derived from @{text "thy"}, initializing all data.
wenzelm@20449
   252
wenzelm@20449
   253
  \item @{ML ProofContext.theory_of}~@{text "ctxt"} selects the
wenzelm@20451
   254
  background theory from @{text "ctxt"}, dereferencing its internal
wenzelm@20451
   255
  @{ML_type theory_ref}.
wenzelm@20449
   256
wenzelm@20449
   257
  \item @{ML ProofContext.transfer}~@{text "thy ctxt"} promotes the
wenzelm@20449
   258
  background theory of @{text "ctxt"} to the super theory @{text
wenzelm@20449
   259
  "thy"}.
wenzelm@20449
   260
wenzelm@20449
   261
  \end{description}
wenzelm@20449
   262
*}
wenzelm@20449
   263
wenzelm@20430
   264
wenzelm@20451
   265
subsection {* Generic contexts \label{sec:generic-context} *}
wenzelm@20429
   266
wenzelm@20449
   267
text {*
wenzelm@20449
   268
  A generic context is the disjoint sum of either a theory or proof
wenzelm@20451
   269
  context.  Occasionally, this enables uniform treatment of generic
wenzelm@20450
   270
  context data, typically extra-logical information.  Operations on
wenzelm@20449
   271
  generic contexts include the usual injections, partial selections,
wenzelm@20449
   272
  and combinators for lifting operations on either component of the
wenzelm@20449
   273
  disjoint sum.
wenzelm@20449
   274
wenzelm@20449
   275
  Moreover, there are total operations @{text "theory_of"} and @{text
wenzelm@20449
   276
  "proof_of"} to convert a generic context into either kind: a theory
wenzelm@20451
   277
  can always be selected from the sum, while a proof context might
wenzelm@20451
   278
  have to be constructed by an ad-hoc @{text "init"} operation.
wenzelm@20449
   279
*}
wenzelm@20430
   280
wenzelm@20449
   281
text %mlref {*
wenzelm@20449
   282
  \begin{mldecls}
wenzelm@20449
   283
  @{index_ML_type Context.generic} \\
wenzelm@20449
   284
  @{index_ML Context.theory_of: "Context.generic -> theory"} \\
wenzelm@20449
   285
  @{index_ML Context.proof_of: "Context.generic -> Proof.context"} \\
wenzelm@20449
   286
  \end{mldecls}
wenzelm@20449
   287
wenzelm@20449
   288
  \begin{description}
wenzelm@20430
   289
wenzelm@20449
   290
  \item @{ML_type Context.generic} is the direct sum of @{ML_type
wenzelm@20451
   291
  "theory"} and @{ML_type "Proof.context"}, with the datatype
wenzelm@20451
   292
  constructors @{ML "Context.Theory"} and @{ML "Context.Proof"}.
wenzelm@20449
   293
wenzelm@20449
   294
  \item @{ML Context.theory_of}~@{text "context"} always produces a
wenzelm@20449
   295
  theory from the generic @{text "context"}, using @{ML
wenzelm@20449
   296
  "ProofContext.theory_of"} as required.
wenzelm@20449
   297
wenzelm@20449
   298
  \item @{ML Context.proof_of}~@{text "context"} always produces a
wenzelm@20449
   299
  proof context from the generic @{text "context"}, using @{ML
wenzelm@20451
   300
  "ProofContext.init"} as required (note that this re-initializes the
wenzelm@20451
   301
  context data with each invocation).
wenzelm@20449
   302
wenzelm@20449
   303
  \end{description}
wenzelm@20449
   304
*}
wenzelm@20437
   305
wenzelm@20476
   306
wenzelm@20476
   307
subsection {* Context data \label{sec:context-data} *}
wenzelm@20447
   308
wenzelm@20447
   309
text {*
wenzelm@20451
   310
  The main purpose of theory and proof contexts is to manage arbitrary
wenzelm@20451
   311
  data.  New data types can be declared incrementally at compile time.
wenzelm@20451
   312
  There are separate declaration mechanisms for any of the three kinds
wenzelm@20451
   313
  of contexts: theory, proof, generic.
wenzelm@20449
   314
wenzelm@20449
   315
  \paragraph{Theory data} may refer to destructive entities, which are
wenzelm@20451
   316
  maintained in direct correspondence to the linear evolution of
wenzelm@20451
   317
  theory values, including explicit copies.\footnote{Most existing
wenzelm@20451
   318
  instances of destructive theory data are merely historical relics
wenzelm@20451
   319
  (e.g.\ the destructive theorem storage, and destructive hints for
wenzelm@20451
   320
  the Simplifier and Classical rules).}  A theory data declaration
wenzelm@20451
   321
  needs to implement the following specification (depending on type
wenzelm@20451
   322
  @{text "T"}):
wenzelm@20449
   323
wenzelm@20449
   324
  \medskip
wenzelm@20449
   325
  \begin{tabular}{ll}
wenzelm@20449
   326
  @{text "name: string"} \\
wenzelm@20449
   327
  @{text "empty: T"} & initial value \\
wenzelm@20449
   328
  @{text "copy: T \<rightarrow> T"} & refresh impure data \\
wenzelm@20449
   329
  @{text "extend: T \<rightarrow> T"} & re-initialize on import \\
wenzelm@20449
   330
  @{text "merge: T \<times> T \<rightarrow> T"} & join on import \\
wenzelm@20449
   331
  @{text "print: T \<rightarrow> unit"} & diagnostic output \\
wenzelm@20449
   332
  \end{tabular}
wenzelm@20449
   333
  \medskip
wenzelm@20449
   334
wenzelm@20449
   335
  \noindent The @{text "name"} acts as a comment for diagnostic
wenzelm@20449
   336
  messages; @{text "copy"} is just the identity for pure data; @{text
wenzelm@20449
   337
  "extend"} is acts like a unitary version of @{text "merge"}, both
wenzelm@20449
   338
  should also include the functionality of @{text "copy"} for impure
wenzelm@20449
   339
  data.
wenzelm@20449
   340
wenzelm@20451
   341
  \paragraph{Proof context data} is purely functional.  A declaration
wenzelm@20451
   342
  needs to implement the following specification:
wenzelm@20449
   343
wenzelm@20449
   344
  \medskip
wenzelm@20449
   345
  \begin{tabular}{ll}
wenzelm@20449
   346
  @{text "name: string"} \\
wenzelm@20449
   347
  @{text "init: theory \<rightarrow> T"} & produce initial value \\
wenzelm@20449
   348
  @{text "print: T \<rightarrow> unit"} & diagnostic output \\
wenzelm@20449
   349
  \end{tabular}
wenzelm@20449
   350
  \medskip
wenzelm@20449
   351
wenzelm@20449
   352
  \noindent The @{text "init"} operation is supposed to produce a pure
wenzelm@20451
   353
  value from the given background theory.  The remainder is analogous
wenzelm@20451
   354
  to theory data.
wenzelm@20449
   355
wenzelm@20451
   356
  \paragraph{Generic data} provides a hybrid interface for both theory
wenzelm@20451
   357
  and proof data.  The declaration is essentially the same as for
wenzelm@20451
   358
  (pure) theory data, without @{text "copy"}, though.  The @{text
wenzelm@20451
   359
  "init"} operation for proof contexts merely selects the current data
wenzelm@20451
   360
  value from the background theory.
wenzelm@20449
   361
wenzelm@20449
   362
  \bigskip In any case, a data declaration of type @{text "T"} results
wenzelm@20449
   363
  in the following interface:
wenzelm@20449
   364
wenzelm@20449
   365
  \medskip
wenzelm@20449
   366
  \begin{tabular}{ll}
wenzelm@20449
   367
  @{text "init: theory \<rightarrow> theory"} \\
wenzelm@20449
   368
  @{text "get: context \<rightarrow> T"} \\
wenzelm@20449
   369
  @{text "put: T \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   370
  @{text "map: (T \<rightarrow> T) \<rightarrow> context \<rightarrow> context"} \\
wenzelm@20449
   371
  @{text "print: context \<rightarrow> unit"}
wenzelm@20449
   372
  \end{tabular}
wenzelm@20449
   373
  \medskip
wenzelm@20449
   374
wenzelm@20449
   375
  \noindent Here @{text "init"} needs to be applied to the current
wenzelm@20449
   376
  theory context once, in order to register the initial setup.  The
wenzelm@20449
   377
  other operations provide access for the particular kind of context
wenzelm@20449
   378
  (theory, proof, or generic context).  Note that this is a safe
wenzelm@20449
   379
  interface: there is no other way to access the corresponding data
wenzelm@20451
   380
  slot of a context.  By keeping these operations private, a component
wenzelm@20451
   381
  may maintain abstract values authentically, without other components
wenzelm@20451
   382
  interfering.
wenzelm@20447
   383
*}
wenzelm@20447
   384
wenzelm@20450
   385
text %mlref {*
wenzelm@20450
   386
  \begin{mldecls}
wenzelm@20450
   387
  @{index_ML_functor TheoryDataFun} \\
wenzelm@20450
   388
  @{index_ML_functor ProofDataFun} \\
wenzelm@20450
   389
  @{index_ML_functor GenericDataFun} \\
wenzelm@20450
   390
  \end{mldecls}
wenzelm@20450
   391
wenzelm@20450
   392
  \begin{description}
wenzelm@20450
   393
wenzelm@20450
   394
  \item @{ML_functor TheoryDataFun}@{text "(spec)"} declares data for
wenzelm@20450
   395
  type @{ML_type theory} according to the specification provided as
wenzelm@20451
   396
  argument structure.  The resulting structure provides data init and
wenzelm@20451
   397
  access operations as described above.
wenzelm@20450
   398
wenzelm@20470
   399
  \item @{ML_functor ProofDataFun}@{text "(spec)"} is analogous to
wenzelm@20470
   400
  @{ML_functor TheoryDataFun} for type @{ML_type Proof.context}.
wenzelm@20450
   401
wenzelm@20470
   402
  \item @{ML_functor GenericDataFun}@{text "(spec)"} is analogous to
wenzelm@20470
   403
  @{ML_functor TheoryDataFun} for type @{ML_type Context.generic}.
wenzelm@20450
   404
wenzelm@20450
   405
  \end{description}
wenzelm@20450
   406
*}
wenzelm@20450
   407
wenzelm@20447
   408
wenzelm@20476
   409
section {* Names *}
wenzelm@20451
   410
wenzelm@20476
   411
text {*
wenzelm@20476
   412
  In principle, a name is just a string, but there are various
wenzelm@20488
   413
  convention for encoding additional structure.  For example, ``@{text
wenzelm@20488
   414
  "Foo.bar.baz"}'' is considered as a qualified name consisting of
wenzelm@20488
   415
  three basic name components.  The individual constituents of a name
wenzelm@20488
   416
  may have further substructure, e.g.\ the string
wenzelm@20488
   417
  ``\verb,\,\verb,<alpha>,'' encodes as a single symbol.
wenzelm@20451
   418
*}
wenzelm@20437
   419
wenzelm@20437
   420
wenzelm@20437
   421
subsection {* Strings of symbols *}
wenzelm@20437
   422
wenzelm@20476
   423
text {*
wenzelm@20476
   424
  \glossary{Symbol}{The smallest unit of text in Isabelle, subsumes
wenzelm@20476
   425
  plain ASCII characters as well as an infinite collection of named
wenzelm@20476
   426
  symbols (for greek, math etc.).}
wenzelm@20470
   427
wenzelm@20476
   428
  A \emph{symbol} constitutes the smallest textual unit in Isabelle
wenzelm@20488
   429
  --- raw characters are normally not encountered at all.  Isabelle
wenzelm@20488
   430
  strings consist of a sequence of symbols, represented as a packed
wenzelm@20488
   431
  string or a list of strings.  Each symbol is in itself a small
wenzelm@20488
   432
  string, which has either one of the following forms:
wenzelm@20437
   433
wenzelm@20451
   434
  \begin{enumerate}
wenzelm@20437
   435
wenzelm@20488
   436
  \item a single ASCII character ``@{text "c"}'', for example
wenzelm@20488
   437
  ``\verb,a,'',
wenzelm@20437
   438
wenzelm@20488
   439
  \item a regular symbol ``\verb,\,\verb,<,@{text "ident"}\verb,>,'',
wenzelm@20476
   440
  for example ``\verb,\,\verb,<alpha>,'',
wenzelm@20437
   441
wenzelm@20488
   442
  \item a control symbol ``\verb,\,\verb,<^,@{text "ident"}\verb,>,'',
wenzelm@20476
   443
  for example ``\verb,\,\verb,<^bold>,'',
wenzelm@20437
   444
wenzelm@20488
   445
  \item a raw symbol ``\verb,\,\verb,<^raw:,@{text text}\verb,>,''
wenzelm@20488
   446
  where @{text text} constists of printable characters excluding
wenzelm@20476
   447
  ``\verb,.,'' and ``\verb,>,'', for example
wenzelm@20476
   448
  ``\verb,\,\verb,<^raw:$\sum_{i = 1}^n$>,'',
wenzelm@20437
   449
wenzelm@20488
   450
  \item a numbered raw control symbol ``\verb,\,\verb,<^raw,@{text
wenzelm@20476
   451
  n}\verb,>, where @{text n} consists of digits, for example
wenzelm@20451
   452
  ``\verb,\,\verb,<^raw42>,''.
wenzelm@20437
   453
wenzelm@20451
   454
  \end{enumerate}
wenzelm@20437
   455
wenzelm@20476
   456
  \noindent The @{text "ident"} syntax for symbol names is @{text
wenzelm@20476
   457
  "letter (letter | digit)\<^sup>*"}, where @{text "letter =
wenzelm@20476
   458
  A..Za..z"} and @{text "digit = 0..9"}.  There are infinitely many
wenzelm@20476
   459
  regular symbols and control symbols, but a fixed collection of
wenzelm@20476
   460
  standard symbols is treated specifically.  For example,
wenzelm@20488
   461
  ``\verb,\,\verb,<alpha>,'' is classified as a letter, which means it
wenzelm@20488
   462
  may occur within regular Isabelle identifiers.
wenzelm@20437
   463
wenzelm@20488
   464
  Since the character set underlying Isabelle symbols is 7-bit ASCII
wenzelm@20488
   465
  and 8-bit characters are passed through transparently, Isabelle may
wenzelm@20488
   466
  also process Unicode/UCS data in UTF-8 encoding.  Unicode provides
wenzelm@20488
   467
  its own collection of mathematical symbols, but there is no built-in
wenzelm@20488
   468
  link to the standard collection of Isabelle.
wenzelm@20476
   469
wenzelm@20476
   470
  \medskip Output of Isabelle symbols depends on the print mode
wenzelm@20476
   471
  (\secref{FIXME}).  For example, the standard {\LaTeX} setup of the
wenzelm@20476
   472
  Isabelle document preparation system would present
wenzelm@20451
   473
  ``\verb,\,\verb,<alpha>,'' as @{text "\<alpha>"}, and
wenzelm@20451
   474
  ``\verb,\,\verb,<^bold>,\verb,\,\verb,<alpha>,'' as @{text
wenzelm@20451
   475
  "\<^bold>\<alpha>"}.
wenzelm@20451
   476
*}
wenzelm@20437
   477
wenzelm@20437
   478
text %mlref {*
wenzelm@20437
   479
  \begin{mldecls}
wenzelm@20437
   480
  @{index_ML_type "Symbol.symbol"} \\
wenzelm@20437
   481
  @{index_ML Symbol.explode: "string -> Symbol.symbol list"} \\
wenzelm@20437
   482
  @{index_ML Symbol.is_letter: "Symbol.symbol -> bool"} \\
wenzelm@20437
   483
  @{index_ML Symbol.is_digit: "Symbol.symbol -> bool"} \\
wenzelm@20437
   484
  @{index_ML Symbol.is_quasi: "Symbol.symbol -> bool"} \\
wenzelm@20547
   485
  @{index_ML Symbol.is_blank: "Symbol.symbol -> bool"} \\
wenzelm@20547
   486
  \end{mldecls}
wenzelm@20547
   487
  \begin{mldecls}
wenzelm@20437
   488
  @{index_ML_type "Symbol.sym"} \\
wenzelm@20437
   489
  @{index_ML Symbol.decode: "Symbol.symbol -> Symbol.sym"} \\
wenzelm@20437
   490
  \end{mldecls}
wenzelm@20437
   491
wenzelm@20437
   492
  \begin{description}
wenzelm@20437
   493
wenzelm@20488
   494
  \item @{ML_type "Symbol.symbol"} represents individual Isabelle
wenzelm@20488
   495
  symbols; this is an alias for @{ML_type "string"}.
wenzelm@20437
   496
wenzelm@20476
   497
  \item @{ML "Symbol.explode"}~@{text "str"} produces a symbol list
wenzelm@20488
   498
  from the packed form.  This function supercedes @{ML
wenzelm@20476
   499
  "String.explode"} for virtually all purposes of manipulating text in
wenzelm@20476
   500
  Isabelle!
wenzelm@20437
   501
wenzelm@20437
   502
  \item @{ML "Symbol.is_letter"}, @{ML "Symbol.is_digit"}, @{ML
wenzelm@20476
   503
  "Symbol.is_quasi"}, @{ML "Symbol.is_blank"} classify standard
wenzelm@20476
   504
  symbols according to fixed syntactic conventions of Isabelle, cf.\
wenzelm@20476
   505
  \cite{isabelle-isar-ref}.
wenzelm@20437
   506
wenzelm@20437
   507
  \item @{ML_type "Symbol.sym"} is a concrete datatype that represents
wenzelm@20488
   508
  the different kinds of symbols explicitly, with constructors @{ML
wenzelm@20488
   509
  "Symbol.Char"}, @{ML "Symbol.Sym"}, @{ML "Symbol.Ctrl"}, @{ML
wenzelm@20451
   510
  "Symbol.Raw"}.
wenzelm@20437
   511
wenzelm@20437
   512
  \item @{ML "Symbol.decode"} converts the string representation of a
wenzelm@20451
   513
  symbol into the datatype version.
wenzelm@20437
   514
wenzelm@20437
   515
  \end{description}
wenzelm@20437
   516
*}
wenzelm@20437
   517
wenzelm@20437
   518
wenzelm@20476
   519
subsection {* Basic names \label{sec:basic-names} *}
wenzelm@20476
   520
wenzelm@20476
   521
text {*
wenzelm@20476
   522
  A \emph{basic name} essentially consists of a single Isabelle
wenzelm@20476
   523
  identifier.  There are conventions to mark separate classes of basic
wenzelm@20476
   524
  names, by attaching a suffix of underscores (@{text "_"}): one
wenzelm@20476
   525
  underscore means \emph{internal name}, two underscores means
wenzelm@20476
   526
  \emph{Skolem name}, three underscores means \emph{internal Skolem
wenzelm@20476
   527
  name}.
wenzelm@20476
   528
wenzelm@20476
   529
  For example, the basic name @{text "foo"} has the internal version
wenzelm@20476
   530
  @{text "foo_"}, with Skolem versions @{text "foo__"} and @{text
wenzelm@20476
   531
  "foo___"}, respectively.
wenzelm@20476
   532
wenzelm@20488
   533
  These special versions provide copies of the basic name space, apart
wenzelm@20488
   534
  from anything that normally appears in the user text.  For example,
wenzelm@20488
   535
  system generated variables in Isar proof contexts are usually marked
wenzelm@20488
   536
  as internal, which prevents mysterious name references like @{text
wenzelm@20488
   537
  "xaa"} to appear in the text.
wenzelm@20476
   538
wenzelm@20488
   539
  \medskip Manipulating binding scopes often requires on-the-fly
wenzelm@20488
   540
  renamings.  A \emph{name context} contains a collection of already
wenzelm@20488
   541
  used names.  The @{text "declare"} operation adds names to the
wenzelm@20488
   542
  context.
wenzelm@20476
   543
wenzelm@20488
   544
  The @{text "invents"} operation derives a number of fresh names from
wenzelm@20488
   545
  a given starting point.  For example, the first three names derived
wenzelm@20488
   546
  from @{text "a"} are @{text "a"}, @{text "b"}, @{text "c"}.
wenzelm@20476
   547
wenzelm@20476
   548
  The @{text "variants"} operation produces fresh names by
wenzelm@20488
   549
  incrementing tentative names as base-26 numbers (with digits @{text
wenzelm@20488
   550
  "a..z"}) until all clashes are resolved.  For example, name @{text
wenzelm@20488
   551
  "foo"} results in variants @{text "fooa"}, @{text "foob"}, @{text
wenzelm@20488
   552
  "fooc"}, \dots, @{text "fooaa"}, @{text "fooab"} etc.; each renaming
wenzelm@20488
   553
  step picks the next unused variant from this sequence.
wenzelm@20476
   554
*}
wenzelm@20476
   555
wenzelm@20476
   556
text %mlref {*
wenzelm@20476
   557
  \begin{mldecls}
wenzelm@20476
   558
  @{index_ML Name.internal: "string -> string"} \\
wenzelm@20547
   559
  @{index_ML Name.skolem: "string -> string"} \\
wenzelm@20547
   560
  \end{mldecls}
wenzelm@20547
   561
  \begin{mldecls}
wenzelm@20476
   562
  @{index_ML_type Name.context} \\
wenzelm@20476
   563
  @{index_ML Name.context: Name.context} \\
wenzelm@20476
   564
  @{index_ML Name.declare: "string -> Name.context -> Name.context"} \\
wenzelm@20476
   565
  @{index_ML Name.invents: "Name.context -> string -> int -> string list"} \\
wenzelm@20476
   566
  @{index_ML Name.variants: "string list -> Name.context -> string list * Name.context"} \\
wenzelm@20476
   567
  \end{mldecls}
wenzelm@20476
   568
wenzelm@20476
   569
  \begin{description}
wenzelm@20476
   570
wenzelm@20476
   571
  \item @{ML Name.internal}~@{text "name"} produces an internal name
wenzelm@20476
   572
  by adding one underscore.
wenzelm@20476
   573
wenzelm@20476
   574
  \item @{ML Name.skolem}~@{text "name"} produces a Skolem name by
wenzelm@20476
   575
  adding two underscores.
wenzelm@20476
   576
wenzelm@20476
   577
  \item @{ML_type Name.context} represents the context of already used
wenzelm@20476
   578
  names; the initial value is @{ML "Name.context"}.
wenzelm@20476
   579
wenzelm@20488
   580
  \item @{ML Name.declare}~@{text "name"} enters a used name into the
wenzelm@20488
   581
  context.
wenzelm@20437
   582
wenzelm@20488
   583
  \item @{ML Name.invents}~@{text "context name n"} produces @{text
wenzelm@20488
   584
  "n"} fresh names derived from @{text "name"}.
wenzelm@20488
   585
wenzelm@20488
   586
  \item @{ML Name.variants}~@{text "names context"} produces fresh
wenzelm@20488
   587
  varians of @{text "names"}; the result is entered into the context.
wenzelm@20476
   588
wenzelm@20476
   589
  \end{description}
wenzelm@20476
   590
*}
wenzelm@20476
   591
wenzelm@20476
   592
wenzelm@20476
   593
subsection {* Indexed names *}
wenzelm@20476
   594
wenzelm@20476
   595
text {*
wenzelm@20476
   596
  An \emph{indexed name} (or @{text "indexname"}) is a pair of a basic
wenzelm@20488
   597
  name and a natural number.  This representation allows efficient
wenzelm@20488
   598
  renaming by incrementing the second component only.  The canonical
wenzelm@20488
   599
  way to rename two collections of indexnames apart from each other is
wenzelm@20488
   600
  this: determine the maximum index @{text "maxidx"} of the first
wenzelm@20488
   601
  collection, then increment all indexes of the second collection by
wenzelm@20488
   602
  @{text "maxidx + 1"}; the maximum index of an empty collection is
wenzelm@20488
   603
  @{text "-1"}.
wenzelm@20476
   604
wenzelm@20488
   605
  Occasionally, basic names and indexed names are injected into the
wenzelm@20488
   606
  same pair type: the (improper) indexname @{text "(x, -1)"} is used
wenzelm@20488
   607
  to encode basic names.
wenzelm@20488
   608
wenzelm@20488
   609
  \medskip Isabelle syntax observes the following rules for
wenzelm@20488
   610
  representing an indexname @{text "(x, i)"} as a packed string:
wenzelm@20476
   611
wenzelm@20476
   612
  \begin{itemize}
wenzelm@20476
   613
wenzelm@20479
   614
  \item @{text "?x"} if @{text "x"} does not end with a digit and @{text "i = 0"},
wenzelm@20476
   615
wenzelm@20476
   616
  \item @{text "?xi"} if @{text "x"} does not end with a digit,
wenzelm@20476
   617
wenzelm@20488
   618
  \item @{text "?x.i"} otherwise.
wenzelm@20476
   619
wenzelm@20476
   620
  \end{itemize}
wenzelm@20470
   621
wenzelm@20488
   622
  Indexnames may acquire large index numbers over time.  Results are
wenzelm@20488
   623
  normalized towards @{text "0"} at certain checkpoints, notably at
wenzelm@20488
   624
  the end of a proof.  This works by producing variants of the
wenzelm@20488
   625
  corresponding basic name components.  For example, the collection
wenzelm@20488
   626
  @{text "?x1, ?x7, ?x42"} becomes @{text "?x, ?xa, ?xb"}.
wenzelm@20476
   627
*}
wenzelm@20476
   628
wenzelm@20476
   629
text %mlref {*
wenzelm@20476
   630
  \begin{mldecls}
wenzelm@20476
   631
  @{index_ML_type indexname} \\
wenzelm@20476
   632
  \end{mldecls}
wenzelm@20476
   633
wenzelm@20476
   634
  \begin{description}
wenzelm@20476
   635
wenzelm@20476
   636
  \item @{ML_type indexname} represents indexed names.  This is an
wenzelm@20476
   637
  abbreviation for @{ML_type "string * int"}.  The second component is
wenzelm@20476
   638
  usually non-negative, except for situations where @{text "(x, -1)"}
wenzelm@20488
   639
  is used to embed basic names into this type.
wenzelm@20476
   640
wenzelm@20476
   641
  \end{description}
wenzelm@20476
   642
*}
wenzelm@20476
   643
wenzelm@20476
   644
wenzelm@20476
   645
subsection {* Qualified names and name spaces *}
wenzelm@20476
   646
wenzelm@20476
   647
text {*
wenzelm@20476
   648
  A \emph{qualified name} consists of a non-empty sequence of basic
wenzelm@20488
   649
  name components.  The packed representation uses a dot as separator,
wenzelm@20488
   650
  as in ``@{text "A.b.c"}''.  The last component is called \emph{base}
wenzelm@20488
   651
  name, the remaining prefix \emph{qualifier} (which may be empty).
wenzelm@20488
   652
  The idea of qualified names is to encode nested structures by
wenzelm@20488
   653
  recording the access paths as qualifiers.  For example, an item
wenzelm@20488
   654
  named ``@{text "A.b.c"}'' may be understood as a local entity @{text
wenzelm@20488
   655
  "c"}, within a local structure @{text "b"}, within a global
wenzelm@20488
   656
  structure @{text "A"}.  Typically, name space hierarchies consist of
wenzelm@20488
   657
  1--2 levels of qualification, but this need not be always so.
wenzelm@20437
   658
wenzelm@20476
   659
  The empty name is commonly used as an indication of unnamed
wenzelm@20488
   660
  entities, whenever this makes any sense.  The basic operations on
wenzelm@20488
   661
  qualified names are smart enough to pass through such improper names
wenzelm@20476
   662
  unchanged.
wenzelm@20476
   663
wenzelm@20476
   664
  \medskip A @{text "naming"} policy tells how to turn a name
wenzelm@20476
   665
  specification into a fully qualified internal name (by the @{text
wenzelm@20488
   666
  "full"} operation), and how fully qualified names may be accessed
wenzelm@20488
   667
  externally.  For example, the default naming policy is to prefix an
wenzelm@20488
   668
  implicit path: @{text "full x"} produces @{text "path.x"}, and the
wenzelm@20488
   669
  standard accesses for @{text "path.x"} include both @{text "x"} and
wenzelm@20488
   670
  @{text "path.x"}.  Normally, the naming is implicit in the theory or
wenzelm@20488
   671
  proof context; there are separate versions of the corresponding.
wenzelm@20437
   672
wenzelm@20476
   673
  \medskip A @{text "name space"} manages a collection of fully
wenzelm@20476
   674
  internalized names, together with a mapping between external names
wenzelm@20476
   675
  and internal names (in both directions).  The corresponding @{text
wenzelm@20476
   676
  "intern"} and @{text "extern"} operations are mostly used for
wenzelm@20476
   677
  parsing and printing only!  The @{text "declare"} operation augments
wenzelm@20488
   678
  a name space according to the accesses determined by the naming
wenzelm@20488
   679
  policy.
wenzelm@20476
   680
wenzelm@20488
   681
  \medskip As a general principle, there is a separate name space for
wenzelm@20488
   682
  each kind of formal entity, e.g.\ logical constant, type
wenzelm@20488
   683
  constructor, type class, theorem.  It is usually clear from the
wenzelm@20488
   684
  occurrence in concrete syntax (or from the scope) which kind of
wenzelm@20488
   685
  entity a name refers to.  For example, the very same name @{text
wenzelm@20488
   686
  "c"} may be used uniformly for a constant, type constructor, and
wenzelm@20488
   687
  type class.
wenzelm@20476
   688
wenzelm@20479
   689
  There are common schemes to name theorems systematically, according
wenzelm@20488
   690
  to the name of the main logical entity involved, e.g.\ @{text
wenzelm@20488
   691
  "c.intro"} for a canonical theorem related to constant @{text "c"}.
wenzelm@20488
   692
  This technique of mapping names from one space into another requires
wenzelm@20488
   693
  some care in order to avoid conflicts.  In particular, theorem names
wenzelm@20488
   694
  derived from a type constructor or type class are better suffixed in
wenzelm@20488
   695
  addition to the usual qualification, e.g.\ @{text "c_type.intro"}
wenzelm@20488
   696
  and @{text "c_class.intro"} for theorems related to type @{text "c"}
wenzelm@20488
   697
  and class @{text "c"}, respectively.
wenzelm@20437
   698
*}
wenzelm@20437
   699
wenzelm@20476
   700
text %mlref {*
wenzelm@20476
   701
  \begin{mldecls}
wenzelm@20476
   702
  @{index_ML NameSpace.base: "string -> string"} \\
wenzelm@20530
   703
  @{index_ML NameSpace.qualifier: "string -> string"} \\
wenzelm@20476
   704
  @{index_ML NameSpace.append: "string -> string -> string"} \\
wenzelm@21862
   705
  @{index_ML NameSpace.implode: "string list -> string"} \\
wenzelm@21862
   706
  @{index_ML NameSpace.explode: "string -> string list"} \\
wenzelm@20547
   707
  \end{mldecls}
wenzelm@20547
   708
  \begin{mldecls}
wenzelm@20476
   709
  @{index_ML_type NameSpace.naming} \\
wenzelm@20476
   710
  @{index_ML NameSpace.default_naming: NameSpace.naming} \\
wenzelm@20476
   711
  @{index_ML NameSpace.add_path: "string -> NameSpace.naming -> NameSpace.naming"} \\
wenzelm@20547
   712
  @{index_ML NameSpace.full: "NameSpace.naming -> string -> string"} \\
wenzelm@20547
   713
  \end{mldecls}
wenzelm@20547
   714
  \begin{mldecls}
wenzelm@20476
   715
  @{index_ML_type NameSpace.T} \\
wenzelm@20476
   716
  @{index_ML NameSpace.empty: NameSpace.T} \\
wenzelm@20476
   717
  @{index_ML NameSpace.merge: "NameSpace.T * NameSpace.T -> NameSpace.T"} \\
wenzelm@20476
   718
  @{index_ML NameSpace.declare: "NameSpace.naming -> string -> NameSpace.T -> NameSpace.T"} \\
wenzelm@20476
   719
  @{index_ML NameSpace.intern: "NameSpace.T -> string -> string"} \\
wenzelm@20476
   720
  @{index_ML NameSpace.extern: "NameSpace.T -> string -> string"} \\
wenzelm@20476
   721
  \end{mldecls}
wenzelm@20437
   722
wenzelm@20476
   723
  \begin{description}
wenzelm@20476
   724
wenzelm@20476
   725
  \item @{ML NameSpace.base}~@{text "name"} returns the base name of a
wenzelm@20476
   726
  qualified name.
wenzelm@20476
   727
wenzelm@20530
   728
  \item @{ML NameSpace.qualifier}~@{text "name"} returns the qualifier
wenzelm@20476
   729
  of a qualified name.
wenzelm@20437
   730
wenzelm@20476
   731
  \item @{ML NameSpace.append}~@{text "name\<^isub>1 name\<^isub>2"}
wenzelm@20476
   732
  appends two qualified names.
wenzelm@20437
   733
wenzelm@21862
   734
  \item @{ML NameSpace.implode}~@{text "name"} and @{ML
wenzelm@21862
   735
  NameSpace.explode}~@{text "names"} convert between the packed string
wenzelm@20488
   736
  representation and the explicit list form of qualified names.
wenzelm@20476
   737
wenzelm@20476
   738
  \item @{ML_type NameSpace.naming} represents the abstract concept of
wenzelm@20476
   739
  a naming policy.
wenzelm@20437
   740
wenzelm@20476
   741
  \item @{ML NameSpace.default_naming} is the default naming policy.
wenzelm@20476
   742
  In a theory context, this is usually augmented by a path prefix
wenzelm@20476
   743
  consisting of the theory name.
wenzelm@20476
   744
wenzelm@20476
   745
  \item @{ML NameSpace.add_path}~@{text "path naming"} augments the
wenzelm@20488
   746
  naming policy by extending its path component.
wenzelm@20437
   747
wenzelm@20476
   748
  \item @{ML NameSpace.full}@{text "naming name"} turns a name
wenzelm@20476
   749
  specification (usually a basic name) into the fully qualified
wenzelm@20476
   750
  internal version, according to the given naming policy.
wenzelm@20476
   751
wenzelm@20476
   752
  \item @{ML_type NameSpace.T} represents name spaces.
wenzelm@20476
   753
wenzelm@20476
   754
  \item @{ML NameSpace.empty} and @{ML NameSpace.merge}~@{text
wenzelm@20488
   755
  "(space\<^isub>1, space\<^isub>2)"} are the canonical operations for
wenzelm@20488
   756
  maintaining name spaces according to theory data management
wenzelm@20488
   757
  (\secref{sec:context-data}).
wenzelm@20437
   758
wenzelm@20476
   759
  \item @{ML NameSpace.declare}~@{text "naming name space"} enters a
wenzelm@20488
   760
  fully qualified name into the name space, with external accesses
wenzelm@20488
   761
  determined by the naming policy.
wenzelm@20476
   762
wenzelm@20476
   763
  \item @{ML NameSpace.intern}~@{text "space name"} internalizes a
wenzelm@20476
   764
  (partially qualified) external name.
wenzelm@20437
   765
wenzelm@20488
   766
  This operation is mostly for parsing!  Note that fully qualified
wenzelm@20476
   767
  names stemming from declarations are produced via @{ML
wenzelm@20488
   768
  "NameSpace.full"} (or its derivatives for @{ML_type theory} and
wenzelm@20488
   769
  @{ML_type Proof.context}).
wenzelm@20437
   770
wenzelm@20476
   771
  \item @{ML NameSpace.extern}~@{text "space name"} externalizes a
wenzelm@20476
   772
  (fully qualified) internal name.
wenzelm@20476
   773
wenzelm@20488
   774
  This operation is mostly for printing!  Note unqualified names are
wenzelm@20476
   775
  produced via @{ML NameSpace.base}.
wenzelm@20476
   776
wenzelm@20476
   777
  \end{description}
wenzelm@20476
   778
*}
wenzelm@20437
   779
wenzelm@18537
   780
end